Below we fix the internal coupling parameter \(\varepsilon =0.075\) .
For \(\varepsilon =0\) , system (REF ) has a stable homoclinic cycle,
where the modes are excited consequentially \(w\rightarrow v\rightarrow u \rightarrow w\rightarrow \ldots \) ,
with increasing periods of the cycle. The effect of coupling \(\varepsilon >0\)  is twofold:
first, the cycle period is limited from above (see Fig. REF (b)),
and second, at each stage where a mode amplitude passes close to zero,
its phase attains the doubled value of the exciting mode. The latter property
is described in Ref. [1]} in details; here
we illustrate it with figure REF . Thus, the KP oscillator (REF )
has a chaotic phase obeying a Bernoulli map.
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